Grating magneto optical trap

ABSTRACT

A three-dimensional magneto-optical trap (3D GMOT) configured to trap a cold-atom cloud is disclosed. The 3D GMOT includes a single input light beam having its direction along a first axis, an area along a second and third axis that are both normal to the first axis, and a substantially flat input light beam intensity profile extending across its area. The 3D GMOT may also include a circular, diffraction-grating surface positioned normal to the first axis and having closely adjacent grooves arranged concentrically around a gap formed in its center. The circular, diffraction-grating surface is configured to diffract first-order light beams that intersect within an intersection region that lies directly above the gap and suppresses reflections and diffractions of all other orders. The 3D GMOT may further include a quadrupole magnetic field with its magnitude being zero within the intersection region.

CROSS-REFERENCE TO RELATED APPLICATIONS

This application claims priority to Unites States Non-provisionalapplication Ser. No. 15/431,492, entitled “Grating Magneto OpticalTrap,” filed Feb. 13, 2017 for Eric Imhof, which claimed priority toUnites States Provisional Application Ser. No. 62/294,454, also entitled“Grating Magneto Optical Trap,” filed Feb. 12, 2016 for Eric Imhof, bothof which are incorporated herein by reference.

GOVERNMENT SPONSORED RESEARCH

This invention was made with government support under contractHQ0147-11-D-0052 awarded by the Air Force Research Laboratory. Thegovernment has certain rights in the invention.

TECHNICAL FIELD

The present disclosure relates to magneto optical traps.

BACKGROUND

A magneto optical trap (MOT) is the primary method by which dilutegasses of atoms and molecules are taken from room temperature to thesub-Kelvin range. It is the first step in many experiments andtechnologies related to high-accuracy atomic clocks, cold atomgyroscopes and accelerometers used in inertial navigation devices,magnetic field sensors, quantum computing, and gravimeters used todetect underground tunnels, aquifers, or other underground naturalresources.

A MOT uses laser beams and magnetic fields to collect a high density ofatoms with low kinetic energy. For example, a three-dimensional MOT cancollect a small cloud, approximately 4 mm across, of super-cooled atomswhere the average speed of an atom in the MOT is on the order of 0.1meters per second. This is compared to atoms at room temperature movingat hundreds of meters per second.

Prior methods of creating three-dimensional MOTs used sixcounter-propagating light beams pointed along the cardinal axes towardsa common intersection to capture cold atoms. See, for example, MatthieuVangeleyn's PhD thesis at the University of Strathclyde, entitled “Atomtrapping in non-trivial geometries for micro-fabrication applications.”Another method replaces two of the six beams with mirrors. Still anothermethod uses a single laser with a corner-cube reflector or reflectingright cone to capture atoms within the reflector.

SUMMARY

The inventor of the present disclosure has identified that presentmethods for creating magneto optical traps (MOT or MOTs) severelyrestrict optical access to the experimental chamber containing the coldatom cloud. Using current methods, lines of sight into the experimentalchamber are blocked by input light beams or reflectors, leaving littleroom for imaging cameras, magnetic field sources, experimental lasers,or other methods of experimentally manipulating the cold atom cloud.Prior methods are also limited in their ability to quickly load a MOTwith a high number of cold atoms necessary to perform cold-atomapplications described above.

The present disclosure in aspects and embodiments addresses thesevarious needs and problems by providing a unique grating magneto opticaltrap (GMOT). Both a two-dimensional (2D) and a three-dimensional (3D)GMOT are described. In embodiments, a 2D GMOT can provide a stream ofcold atoms that can be captured in a 3D GMOT above a planar surface,loading the 3D GMOT much more quickly and enabling the experimenter tointeract from all sides without obstruction. Additionally, the GMOTrequires less laser power as compared to other MOTs. Also, most of thedesign requirements for a working MOT are satisfied through the designof the grating, alleviating many concerns about alignment, cost, size,and reproducibility. Finally, experimental results of the GMOT show ahigh-atom number and the ability to perform sub-Doppler cooling.

The benefits of using gratings apply equally well to a 3D GMOT as a 2DGMOT. If loaded by a cold atom beam from a 2D GMOT, a 3D GMOT is acompelling source for cold atom experiments. The atomic beam from a 2DGMOT enables higher atom number and loading rates in the 3D GMOT byseparating the source vapor from the experimental region.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 illustrates the input, reflected, and diffracted light beams of atwo-dimensional magneto optical trap (2D GMOT);

FIG. 2 illustrates the quadrupole magnetic field of a 2D GMOT;

FIG. 3 illustrates the input, reflected, and diffracted light beams ofanother 2D GMOT;

FIG. 4 illustrates a directed input light beam and the correspondingreflected, and diffracted light beams of a 2D GMOT;

FIG. 5 illustrates the input, reflected, and diffracted light beams of athree-dimensional magneto optical trap (3D GMOT);

FIG. 6 illustrates a portion of the quadrupole magnetic field of a 3DGMOT;

FIG. 7 illustrates another 3D GMOT;

FIG. 8 illustrates a 2D GMOT providing a stream of atoms to a 3D GMOT;and

FIGS. 9 and 10 illustrate black and white photographs illustrating theactual results of a 2D GMOT and a 3D GMOT, respectively.

DETAILED DESCRIPTION

The present disclosure covers apparatuses and associated methods forgrating magneto optical traps (GMOTs). In the following description,numerous specific details are provided for a thorough understanding ofspecific preferred embodiments. However, those skilled in the art willrecognize that embodiments can be practiced without one or more of thespecific details, or with other methods, components, materials, etc. Insome cases, well-known structures, materials, or operations are notshown or described in detail in order to avoid obscuring aspects of thepreferred embodiments. Furthermore, the described features, structures,or characteristics may be combined in any suitable manner in a varietyof alternative embodiments. Thus, the following more detaileddescription of the embodiments of the present invention, as illustratedin some aspects in the drawings, is not intended to limit the scope ofthe invention, but is merely representative of the various embodimentsof the invention.

In this specification and the claims that follow, singular forms such as“a,” “an,” and “the” include plural forms unless the content clearlydictates otherwise. All ranges disclosed herein include, unlessspecifically indicated, all endpoints and intermediate values. Inaddition, “optional,” “optionally,” or “or” refer, for example, toinstances in which subsequently described circumstance may or may notoccur, and include instances in which the circumstance occurs andinstances in which the circumstance does not occur. The terms “one ormore” and “at least one” refer, for example, to instances in which oneof the subsequently described circumstances occurs, and to instances inwhich more than one of the subsequently described circumstances occurs.

FIG. 1 illustrates light beams and a diffraction grating of a 2D GMOT100. In embodiments, a single input light beam 10 is directed along afirst axis, in this figure labeled the z-axis. Input light beam 10 has awidth 10 c along a second axis, in this figure labeled the x-axis. Inputlight beam 10 also has an ideal intensity profile 10 a distributedacross the input light beam width 10 c. In practice, input light beam'sintensity profile is more like the Gaussian-shaped intensity profile 10b. The intensity profile 10 a or 10 b is intentionally made to besubstantially flat or uniform across the width 10. In this disclosure, asubstantially flat or uniform intensity profile means that the intensityof one part of input light beam 10 is substantially equal to anotherpart of input light beam 10 across the effective width 10 c of the lightbeam 10.

2D GMOT 100 also includes a diffraction grating 2 with a diffractiongrating surface 2 a. The diffraction-grating surface 2 a is positionednormal to the first axis, or normal to the incident, input light beam10. The diffraction-grating surface is also comprised of closelyadjacent parallel grooves 2 b spread across the width 10 c of inputlight beam 10. In this embodiment, the closely adjacent parallel grooves2 b run parallel to the third axis. The third axis is normal to both thefirst and second axes, labeled the y-axis in the figures.

The diffraction grating surface 2 a reflects zeroth order light beams 12b and diffracts first-order and other order light beams 12 a and 12 c,respectively. In embodiments, the diffraction grating surface 2 adiffracts first-order light beams that intersect within an intersectionplane 20 that lies within a plane defined by the first and second axis.In this configuration, the input light beam 10 also intersects with thefirst-order light beams 12 a at the intersection plane 20.

The cooling of atoms in a magneto-optical trap occurs through Dopplercooling. Opposing beams of light with the correct frequency andpolarization may strike an atom such that the atom absorbs a photon andreceives a small push in the direction of the striking light beam.

In embodiments, the relative light intensities of the input light beam10 and the first-order diffracted light beams 12 a are configured toprovide the necessary forces to help push atoms towards the center ofthe intersection plane 20. In other words, for a trap to form, the sumof the forces on the atoms should be approximately zero. Accordingly,I_(up)=I₁/n cos θ, where I_(up) is the upward intensity from thediffracted first-order light beams 12 a, I₁ is the intensity of thesingle input light beam 10, n is the number of diffracted first-orderlight beams 12 a (in the case of this 2D GMOT embodiment, n equals two),and θ is the angle of the diffracted first-order light beams 12 a (inthe case of this 2D GMOT embodiment, θ equals 45). Additionally, thediffracted first order light beams 12 a are spatially compressed,meaning their intensity is greater within a smaller area, by a factor ofcos θ. Thus, in the case of the 2D GMOT described herein, I_(up)=I₁/2,or the diffracted first order light beams 12 a should have an intensitythat is roughly 50% of the single input light beam 10.

In addition, in this embodiment, the diffraction grating surface 2 asuppresses reflections 12 b and diffractions of all other order lightbeams 12 c. As such, the inventor of the present disclosure has foundthat small deviations, on the order of +/−10%, in the intensity ratio(between the diffracted first order light beams 12 a and the singleinput light beam 10) still produces a trap but moves the location of thetrap with respect to the magnetic field zero. Thus, a trap may still beformed when the diffracted first-order light beams' intensity is betweenroughly 40 and 60% of the incoming light beam's intensity. Thereflection suppression by the diffraction grating surface 2 a and theintensity matching of the incoming light beam 10 and first-orderdiffracted light beams 12 a provide a combined force that helps pushatoms towards the center of the magneto-optical trap 100 or the centerof the intersection plane 20.

Doppler cooling alone will slow the motion of an atom but it will notreverse an atom's direction of travel or, in the case of amagneto-optical trap 100, collect cold atoms at the center of theintersection plane 20. Once an atom stops moving, it sees no Dopplershift and will no longer absorb photons from the input light beam 10 orthe first-order diffracted light beams 12 a. The presence of a magneticfield is necessary to trap atoms at the center of the intersection plane20.

Magneto-optical trap 100 further comprises a quadrupole magnetic field.For clarity purposes, the quadrupole magnetic field that is part of themagneto-optical trap 100 is not shown in FIG. 1 but is shown in FIG. 2with its position relative to the intersection plane 20. A magneticfield at any given point may be specified as having both a direction anda magnitude. However, if the magnitude is zero at a given point, thedirection is also zero. FIG. 2 shows the quadrupole magnetic field 40with its force and direction being zero at the center of theintersection plane 20. In this embodiment, the quadrupole magnetic field40 has a magnitude of zero along the third axis and is centered at thecenter of the input light beam's width 10 c, or at the center of theintersection plane 20.

FIG. 3 illustrates another embodiment of a magneto-optical trap 200. Inthis embodiment, the diffraction-grating surface is comprised of twodiffraction grating surfaces 4 a and 4 b separated by a gap 4 c, whichis formed by the separation between the diffraction grating surfaces 4 aand 4 b. The gap 4 c extends parallel to the third axis and is centered,relative to the second axis, at the center of the intersection plane 20.

The diffraction grating surfaces 4 a and 4 b in 2d GMOT trap 200 neednot suppress reflections and diffractions of all other orders because ofthe gap 4 c between the surfaces 4 a and 4 b. In this embodiment, inputlight beam 10 is not reflected back into the intersection plane 20 butinstead passes through the gap 4 c. Instead, this embodiment may use aless expensive or lower quality diffraction grating while achieving thesame atom trapping results.

The 2D GMOTs 100 and 200 do not constrain atom movement along the thirdaxis. As such, in embodiments, a magneto optical trap such as magnetooptical trap 100 or 200 provides a stream of cooled atoms or an atombeam 16 flowing along the third axis that may feed into athree-dimensional magneto-optical trap (3D GMOT).

FIG. 4 illustrates a side-view of another magneto optical trap 300. Inthis embodiment, the input light beam 10 has a vector component 10 ythat is parallel to the third axis. Vector component 10 y helps producea stream of cooled atoms or an atom beam 16 flowing in the samedirection as the vector component 10 y.

The vector component 10 y points opposite the atom beam 16 direction toprovide Doppler cooling along the beam 16. This may be done by having abeam opposite along 10 y with a mirror reflecting the beam back onto theatom beam (i.e. the mirror, not shown, would be on the far right of thefigure). The mirror would have a small hole in it through which the atombeam 16 could pass. Alternatively, in another embodiment, there is nomirror but just an angled beam 10 such that vector 10 y is opposite theatom beam 16.

FIG. 5 illustrates a 3D GMOT 400. Like the 2D GMOTs 100 and 200, 3D GMOT400 includes an input light beam 10 directed along a first axis, labeledthe z-axis in FIG. 5. Input light beam 10 has an area 10 d extending ina second and third axis, the second and third axes are perpendicular tothe first axis and labeled as the x and y-axis in FIG. 5. Input lightbeam 10 in FIG. 5 might have a similar intensity profile across the area10 d as the intensity profile 10 a described in relation to 2D GMOTs 100and 200 illustrated in FIGS. 1 and 3.

FIG. 5 further illustrates diffraction gratings 6 a, 6 b, 6 c, and 6 dwith their respective diffraction grating surfaces. The diffractiongrating surfaces of 6 a, 6 b, 6 c, and 6 d are comprised of closelyadjacent parallel grooves (not shown) that run substantially parallel totheir longest outside edge of their respective diffraction gratingsurface. In other words, the adjacent parallel grooves of diffractiongratings 6 a and 6 c run along the x-axis and the adjacent parallelgrooves of diffraction gratings 6 b and 6 d run along the y-axis, asillustrated in FIG. 5.

Diffraction gratings 6 a, 6 b, 6 c, and 6 d are combined to form a gap 6e at the center of the diffraction gratings 6 a, 6 b, 6 c, and 6 d. Thegap 6 e prevents the reflection of zeroth order light beams (not shown)directly above the gap (along the z-axis).

As in the 2D GMOTS 100, 200, and 300, the cooling of atoms in the 3DGMOT 400 occurs through Doppler cooling. Opposing beams of light withthe correct frequency and polarization may strike an atom such that theatom absorbs a photon and receives a small push in the direction of thestriking light beam.

Diffraction gratings 6 a, 6 b, 6 c, and 6 d diffract first-order lightbeams 12 a. In embodiments, the diffracted first-order light beams 12 aand the single input light beam 10 intersect at an intersection region22 above the gap 6 e formed between the surfaces of the diffractiongratings 6 a, 6 b, 6 c, and 6 d. A cold atom cloud 18 forms within theintersection region 22.

As in the case of the 2D GMOT described above, with respect to the 3DGMOT, the relative light intensities of the input light beam 10 and thefirst-order diffracted light beams 12 a are configured to provide thenecessary forces to help push atoms towards the center of theintersection region 22. In other words, for a trap to form, the sum ofthe forces on the atoms should be approximately zero. Accordingly,I_(up)=I₁/n cos θ, where I_(up) is the upward force from the diffractedfirst-order light beams 12 a, I₁ is the force exerted by the singleinput light beam 10, n is the number of diffracted first-order lightbeams 12 a (in the case of this 3D GMOT embodiment, n equals four, sincethere are four diffraction grating surfaces), and θ is the angle of thediffracted first-order light beams 12 a (in the case of this 3D GMOTembodiment, 0 equals 45). Additionally, the diffracted first order lightbeams 12 a are spatially compressed, meaning their intensity is greaterwithin a shorter area, by a factor of cos θ. Thus, in the case of the 3DGMOT described herein, I_(up)=I₁/4, or the diffracted first order lightbeams 12 a should have an intensity that is roughly 25% of the singleinput light beam 10.

In addition, in this embodiment, the diffraction grating surface 2 asuppresses reflections 12 b and diffractions of all other order lightbeams 12 c. As such, the inventor of the present disclosure has foundthat small deviations, on the order of +/−10%, in the intensity ratio(between the diffracted first order light beams 12 a and the singleinput light beam 10) still produce a trap but move the location of thetrap with respect to the magnetic field zero. Thus, a trap may still beformed when the diffracted first-order light beams' intensity is betweenroughly 15 and 35% of the incoming light beam's intensity. Thereflection suppression by the diffraction grating surface 2 a and theintensity matching of the incoming light beam 10 and first-orderdiffracted light beams 12 a provide a combined force that helps pushatoms towards the center of the magneto-optical trap 400 or the centerof the intersection region 22.

3D GMOT 400 further comprises a quadrupole magnetic field. For claritypurposes, the quadrupole magnetic field that is part of themagneto-optical trap 400 is not shown in FIG. 5 but a portion of it isshown in FIG. 6, with its position relative to the intersection region22 and the diffraction gratings 6 a, 6 b, 6 c, and 6 d. A magnetic fieldat any given point may be specified as having both a direction and amagnitude. However, if the magnitude is zero at a given point, thedirection is also zero. For clarity purposes, FIG. 6 does not show allthe field vectors of the quadrupole magnetic field 40. However, theforce and direction of quadrupole magnetic field 40 are zero at thecenter of the intersection region 20, or the center 42 of the quadrupolemagnetic field 40 is zero.

In other embodiments, FIG. 7 illustrates 3D GMOT 500 with a circulardiffraction grating 7, diffraction grating surface 7 a, and a hole 7 bformed in the center of the diffraction grating 7. Diffraction gratingsurface 7 a comprises closely concentric circular grooves.

Like previous GMOTs disclosed herein, 3D GMOT 500 comprises a singleinput light beam 10 directed along a first axis, labeled the z-axis inFIG. 7. Input light beam 10 has an area 10 d extending in a second andthird axis, the second and third axis being perpendicular to the firstaxis and labeled as the x and y-axis in FIG. 7. Input light beam 10 inFIG. 7 might have a similar intensity profile across the area 10 c asthe intensity profile described in relation to FIGS. 1, 3, and 5.

Diffraction grating 7 forms a hole in its center. The hole 7 preventsthe reflection of zeroth order light beams (not shown) directly abovethe gap (along the z-axis).

Diffraction grating 7 diffracts first-order light beams 12 a. Inembodiments, the diffracted first-order light beams 12 a and the inputlight beam 10 intersect at an intersection region 22 above the hole 7formed at the center of diffraction grating 7. A cold atom cloud 18forms within the intersection region 22.

Similar to 3D GMOT 400, 3D GMOT 500 comprises a quadrupole magneticfield that is not shown, however, its description is similar to thatdescribed in relation to quadrupole magnetic field 40 illustrated inFIG. 6.

FIG. 8 illustrates a 2D GMOT, such as 2D GMOTs 100, 200, or 300,providing a stream of atoms 16 that is captured by a 3D GMOT, such as 3DGMOT 400 or 500. FIG. 8 further illustrates a single input light beam 10for each of the 2D and 3D GMOTS. As can be seen in FIG. 8, the 2D and 3DGMOTs are configured to enable an experimenter to interact from allsides of the GMOTs without obstruction from other input light sources orother lab equipment necessary to form an atomic beam or an atomic cloud.Additionally, the GMOT configurations illustrated in FIG. 8 require lesslaser power as compared to other MOTs that have multiple input lightbeams.

In FIG. 8, the 2D GMOT 100, 200, or 300 resides in vacuum cell 30 andthe 3D GMOT 400 or 500 resides in a second vacuum cell 32. The 2D GMOT100, 200, or 300 may be capped by a silicon reflector with a pinhole(not shown). The atom beam 16 travels through the pinhole from the 2DGMOT 100, 200, or 300 to the 3D GMOT 400 or 500. The atomic beam 16 fromthe 2D GMOT 100, 200, or 300 enables higher atom number capture andloading rates in the 3D GMOT 400 or 500 by separating the source vapor(in vacuum cell 30) from the experimental region (in vacuum cell 32).Separating the source vapor from the experimental region in thisconfiguration further enables greater access by an experimenter to theexperimental region.

FIGS. 9 and 10 are black and white photographs illustrating the actualresults of a 2D and 3D GMOTs, respectively. FIG. 9 shows a 2D GMOTproducing an atom beam (shown as the white region). FIG. 10 shows a 3DGMOT producing an atom cloud (also shown as a white region or cloud).

The following examples are illustrative only and are not intended tolimit the disclosure in any way.

Examples

The inventor of the present disclosure built functional two-dimensionaland three-dimensional grating magneto-optical trap (2D and 3D GMOTs).This included a vacuum chamber of bonded anti-reflection coatedborosilicate glass. The six-sided, rectangular chamber measured 89×32×35mm, with a large hole cut into one of the 32×35 mm faces which wasbonded to a vacuum pumping system. One of the 89×32 mm faces of thechamber was a 1 mm thick sapphire wafer. The evacuated chamber operatedat pressures low as 10⁻⁹ Torr, or lower.

The relatively high (45%) efficiency requirements of the 2D GMOTpreclude many grating types. Any grating without a preferred directionwould have to diffract practically all input into the +/− first orders.

Non-direction etched gratings have been fabricated to this standard,albeit with a high input of design time and fabrication cost. Suchgratings often require e-beam lithography for small (≈500 nm) featureseizes. E-beam lithography for large area gratings monopolizesclean-room facilities making them prohibitively expensive.

Replicated blazed gratings are inexpensive, but design choices areconfined to commercially produced masks. Additionally, these gratingsare not designed to minimize reflections, which can undermine trapperformance by producing an additional beam with a typicallyanti-trapping polarization. GMOT designs with blazed gratings have gapsbetween gratings along the central axis to allow light to pass (as shownin FIGS. 3, 5, and 6).

The inventor obtained two 45×12 mm, 18-degree blazed diffractiongratings, with parallel grooves along the long axis at 900 grooves/mmand 1000 nm-blaze wavelength, with equal linear polarizationefficiencies near 60%. The equal linear polarization resulted in acircularly polarized diffracted beam. The inventor placed the gratingsurfaces against the glass surface opposite the sapphire wafer. Thegratings were aligned parallel to the 89-mm axis of the vacuum chamberand separated from each other by 5 mm. The blazes were oriented towardsthe gap separating the gratings.

The inventor then dispensed ⁸⁷Rb atoms into the chamber. A laser andamplifier system produced coherent light at 780.246 nm wavelength, whilea separate laser produced coherent light at 780.232 nm wavelength. Thetwo beams were combined, linearly polarized, and input into a commonpolarization-maintaining optical fiber. The fiber output 70 mW ofoptical power at 780.236 nm and 12 mW at 780.232 nm. The light wasexpanded with two-inch optics and circularly polarized before beingdirected through the sapphire window, into the chamber, and towards thegratings.

The light diffracted off the gratings at an angle of 44.5 degrees. Theintensity of the light impinging on the grating was diffracted into theblaze-preferred first order with an overall efficiency near 60%. Thediffracted light was mostly of the opposite circular polarization as theinput beam. A region of space was formed inside the vacuum chamber inwhich the input and preferred first order beams overlapped. Thecross-sectional area of this region was approximately 6 mm².

A two-dimensional quadrupole magnetic field was generated using four2×0.125×0.25 inch permanent magnets arranged at the corners of thevacuum chamber. The two-inch magnet axes were parallel to the 89-mm axisof the chamber. The main axis of the field was directed along thedirection of the input light beam. The location where the magnetic fieldwas zero was set within the overlapping area of the input and diffractedlight beams. The gradient of the field near the zero location was 30G/cm.

The existence of a 2D-GMOT was verified by observing the atomicfluorescence with a CCD camera imaging the plane of the overlappingbeams (as shown in FIG. 8). The high atomic density at the center of themagnetic field was evidenced by a high fluorescence at that location.The high-density region could be moved by displacing the magneticfield's zero region. Additionally, the density could be optimized byshifting the input light's circular polarization. The high-densityregion disappeared when the 780.232 nm light was removed. These factorsare indicative of a magneto-optical trap.

In another experimental setup, the inventor of the present disclosureused two glass vacuum cells separated by a mini-conflat flange. The 2DGMOT was produced in a chamber 30×40×72 mm³, which is capped by asilicon reflector with a 1 mm-diameter pinhole. The atom beam traveledthrough the pinhole, through a second filtering 3 mm pinhole in thecopper gasket of the conflat cross. The atoms were then collected on theopposing side of the cross in a 3D GMOT in a chamber that is 25×40×85mm³. All glass walls were anti-reflection coated on both sides at 780nm.

In this experiment, the inventor located the gratings outside the vacuumchamber. The added optical path through the glass chamber surfacemodifies the intensity and polarization of the diffracted beams. As aresult, the inventor used gratings with 830 grooves/mm for 800 nmwavelength. A normally incident, circularly polarized beam input beamdiffraction through the chamber wall will have 64% of the originalintensity and be 90% polarized with the opposite handedness.

In this same experiment, for the 2D GMOT, the inventor used two 17.5×38mm² rectangular gratings with their blazes facing towards their commonaxis, separated by a 5-mm gap. For the 3D GMOT, the inventor used fourtrapezoidal gratings such that when combined they produced a 38×38 mm²square with a 4×4 mm² gap at its center (as illustrated in FIG. 5).Again, all the blazes point towards the central axis. However, the 3DGMOT requires an efficiency closer to 25%. To reduce the diffracted beampower, a 0.1 ND filter was placed between the gratings and the vacuumchamber wall.

A single laser beam was input into each chamber. Each beam carried 11.0mW/cm² light at the cooling (detuned 5²S_(1/2)→5²S_(3/2), F=2→3, Δ=−1.3Γ) transition and 3.8 mW/cm² (F=1→2) at the repump transition for ⁸⁷Rb.The light was emitted from a single mode, polarization-maintaining fiberand expanded through a negative lens. A wide-angle quarter wave plateprovides circular polarization to the expanding beam, which is thenreflected from a two-inch mirror and collimated with a 100-mm focallength lens.

A “push” beam was directed along the 2D GMOT axis to provide enhancedcooling, using 3.3 mW of cooling light in a beam with a 4-mm waist. Thebeam was retro-reflected using a silicon mirror.

The 2D GMOT magnetic fields were provided by four permanent neodymiummagnets arranged on cage rods outside the chamber. They were positionedvia a three-axis translation stage and a tip-tilt mirror mount to aidalignment of the 2D GMOT with the silicon pinhole. They provided anextended quadrupole field with a 20 G/cm gradient.

The 3D GMOT magnetic fields were produced by an anti-Helmholtz coilpair, centered by the cage rods that aligned the 3D GMOT optics. Runninga 1.2 A current, they provided a gradient of 10 G/cm in the axialdirection.

The system was evacuated to a pressure of 2×10⁻⁹ Torr, measured using aresidual gas analyzer.

The 3D GMOT fluorescence was monitored using a photodiode from Thorlabs(PDA100A). Light from the GMOT was collected using a f=25.4 mm lenspositioned 2 f from the trap and the sensor surface.

Pulsing the 3D GMOT's magnetic field off and on produced a risingfluorescence signal proportional to the number of captured atoms. Bymonitoring the 3D GMOT fluorescence as a function of time, the 2D GMOTbeam could be characterized. An 8-mW “plug” laser beam was positionedjust after the exit pinhole. The beam acted to misalign the atomic beamfrom the 2D GMOT, which reduced the capture rate of the atoms. When theplug beam was turned off for a short period, the 3D GMOT would grow asatoms traversed the distance from the exit pinhole to the 3D GMOT atomiccloud.

It will be appreciated that various of the above-disclosed and otherfeatures and functions, or alternatives thereof, may be desirablycombined into many other different systems or applications. Also,various presently unforeseen or unanticipated alternatives,modifications, variations or improvements therein may be subsequentlymade by those skilled in the art, and are also intended to beencompassed by the following claims.

I claim:
 1. A three-dimensional grating magneto optical trap (3D GMOT)comprising: a single input light beam having its direction along a firstaxis, an area along a second and third axis that are both normal to thefirst axis, and a substantially flat input light beam intensity profileextending across its area; a circular, diffraction-grating surfacepositioned normal to the first axis and extending along the second andthird axis; the circular, diffraction-grating surface having closelyadjacent grooves arranged concentrically around a gap formed in thecenter of the circular, diffraction-grating surface; the circular,diffraction-grating surface configured to: diffract first-order lightbeams that intersect within an intersection region that lies directlyabove the gap, and suppresses reflections and diffractions of all otherorders; and a quadrupole magnetic field with its magnitude being zerowithin the intersection region; wherein the 3D GMOT is configured totrap a cold-atom cloud within the intersection region.
 2. The 3D GMOT ofclaim 1, wherein each of the diffracted first-order light beam'sintensity is between 15 and 35% of the input light beam's intensity. 3.A method for trapping a cold-atom cloud, the method comprising providinga three-dimensional grating magneto optical trap (3D GMOT), comprising:providing a first, single input light beam having its direction along afirst axis, an area along a second and third axis that are both normalto the first axis, and a substantially flat input light beam intensityprofile extending across its area; providing a circular,diffraction-grating surface positioned normal to the first axis andextending along the second and third axis; the circular,diffraction-grating surface having closely adjacent grooves arrangedconcentrically around a gap formed in the center of the circular,diffraction-grating surface; the circular, diffraction-grating surfaceconfigured to: diffract first-order light beams that intersect within anintersection region that lies directly above the gap, and suppressesreflections and diffractions of all other orders; and providing aquadrupole magnetic field with its magnitude being zero within theintersection region; wherein the 3D GMOT is configured to trap thecold-atom cloud within the intersection region.
 4. The method of claim3, wherein each of the diffracted first-order light beam's intensity isbetween 15 and 35% of the input light beam's intensity.